Big Ideas 4 - 6 Session 3

1. Big Ideas 4 - 6Session 3

2. Continuing with.. Tonight we will finish our work with number operations and go on to patterns and relations and statistics and probability.

3. Alternate algorithms We ended last time talking about the value of alternate strategies (or algorithms).

4. Would you… • calculate 532 – 99 the same way you would calculate 532 – 111? • Use a √ for yes and an x for no.

5. Would you… • calculate 532 – 99 the same way you would calculate 532 – 111? • Use a √ for yes and an x for no. • Should students?

6. 22 x 13 20 2 10 3 200 20 60 6 • Here are two ways to represent 22 x 13. 22 x13 66 +220 286 Which one do you prefer? Use √ for the left and x for the right.

7. What about division? Let’s think about both • what it means and • how to calculate

8. Which representation? Which picture best shows what 72 ÷ 3 means? (You will vote soon.)

9. Which representation? Which picture best shows what 72 ÷ 3 means? (You will vote soon.)

10. Vote • A for 1st picture • B for 2nd picture • C if you think they’re equally good • D if you think neither is good I will ask a few people to explain their thinking.

11. And what procedure? What do each of the procedures on the next screen help a student see better than the other ones? Vote A,B or C to tell me which you are willing to talk about in terms of what is good about it. I will call on people in each category.

12. 115 ÷ 5 23 10 + 10 + 3 5 115 5 115 5 50 + 50 + 15 -100 - 50 10 15 65 - 15- 50 10 0 15 - 15 3 0 23

13. What about estimating? Let’s think about estimating questions. It’s no longer just about rounding rules. Consider these questions.

14. I added…. 3 numbers. One is little. One is close to double the other. The sum is 5000. What could the numbers be? Type your numbers on next empty screen.

16. I subtracted… a number from 3000. The result had the digits 3 and 4 in it. What could the subtraction have been? Write some numbers on next empty screen.

18. The product is.. • The product of two numbers is almost 400. • What might the numbers be? Raise your hand to respond.

19. I wonder.. • I divided []3[] by 4. • The answer was a 3 digit number. • Tell me anything about []3[] that you’re sure of. Raise your hand to respond.

21. Patterns

22. WNCP Pattern Outcomes Grade 4- focus on identifying patterns and relationships in tables and charts Grade 5- focus on pattern rule to predict Grade 6- focus on table of value relationships

23. Here is a multiplication table

24. Here is a multiplication table

25. Big Idea

26. Here is a multiplication table

27. Big idea

28. Look at this 0 9 1 2 8 3 7 4 6 5 • To show the final digits of the multiples of 8:

29. Look at this 0 9 1 2 8 3 7 4 6 5 • To show the final digits of the multiples of 6. Someone take the pen.

30. Another big idea

31. Or another pattern

32. 1 x 2 + 2 x 3 1 x 3 + 2 x 3 3 x 1 + 4 x 2 3 x 2+ 4 x 1

33. Move objects to compare 3 x 3 + 4 x 4 to 3 x 4 + 4 x 3

34. Picture a 100 chart

35. Big Idea

36. How else could you… • represent the pattern 2, 5, 8, 11,….

37. How else could you… • represent the pattern 2, 5, 8, 11,….

38. How else could you… • represent the pattern 2, 5, 8, 11,….

39. How else could you… • What pattern do you see? Term number Term value 1 2 2 5 3 8 4 11

40. How else could you… • What pattern do you see? Term number Term value Related pattern 1 2 3 2 5 6 3 8 9 4 11 12

41. Variables and equations Grade 4- problems as equations with unknowns; solve one-step equations Grade 5- single-variable, one-step equations Grade 6- generalizations written using variables; model equality preservation

42. Algebra big ideas

43. Try this What situation might 2w describe? Type some possibilities on the next screen.

45. Try this • Jeff got $12 in allowance every week. • What does 6 x w tell about the situation? A: his allowance B: his allowance in w weeks C: his allowance in 2 xw weeks D: his allowance in w ÷ 2 weeks

46. Try this Jeff got $12 in allowance every week. What does 12w tell about the situation? What equation would you solve to find out how many weeks until he had $156?

47. The solution is… The solution to an equation is x = 2. What might the equation have been? Type some possibilities on the next screen.

49. Respond by raising your hand

50. Data • Grade 4- many-to-one correspondence for pictographs and bar graphs • Grade 5- double bar graphs • Grade 6- line graphs